Question

the order of these transformations under the two sets of transformations. matter because the images are reflect triangle def over the x - axis, then translate the image 2 units left. then, reverse the order of those transformations to determine whether the order mattered.

Explanation:

Step1: Recall transformation rules

Reflection over x - axis changes (x,y) to (x, - y). Translation 2 units left changes (x,y) to (x - 2,y).

Step2: First reflect then translate

Let a point on triangle DEF be (x,y). After reflection over x - axis, it becomes (x, - y). Then after translation 2 units left, it becomes (x - 2, - y).

Step3: First translate then reflect

If we first translate (x,y) 2 units left, it becomes (x - 2,y). Then after reflection over x - axis, it becomes (x - 2, - y).

Answer:

The order does not matter.